A symmetric frame $$PQR$$ consists of two inclined members $$PQ$$ and $$QR$$, connected at $$‘Q’$$ with a rigid joint, and hinged at $$‘P’$$ and $$‘R’.$$ The horizontal length $$PR$$ is $$l.$$ If a weight $$W$$ is suspended at $$‘Q’,$$ the bending moment at $$‘Q’$$ is

A three hinged parabolic arch having a span of $$20$$ $$m$$ and a rise of $$5$$ $$m$$ carries a point load of $$10$$ $$kN$$ at quarter span from the left end as shown in the figure. The resultant reaction at the left support and its inclination with the horizontal are respectively

A three hinged parabolic arch $$ABC$$ has a span of $$20$$ $$m$$ and a central rise of $$4$$ $$m.$$ The arch has hinges at the ends and at the center. A train of two point loads of $$20$$ $$kN$$ and $$10$$ $$kN$$, $$5$$ $$m$$ apart, crosses this arch from left to right, with $$20$$ $$kN$$ load leading. The maximum thrust induced at the supports is

A three hinged arch shown in Figure is quarter of a circle. If the vertical and horizontal components of reaction at $$A$$ are equal, the value of $$\theta $$ is